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IEEE Texas Power and Energy Conference (TPEC)

Quantum-Enhanced DC Optimal Power Flow

Farshad Amani, Reza Mahroo, Amin Kargarian

Published Feb 13, 2023• 15 citations
Publisher

Abstract

Harrow-Hassidim-Lloyd (HHL) is a quantum computation algorithm that can solve a system of linear equations in a logarithmic time scale; hence, an exponential speed-up over best-known classical computers, which have polynomial time complexity, is accessible. This paper studies the integration of HHL into the DC optimal power flow problem. Optimality conditions are formulated as a system of equations in the form of $Ax=b$ that is solved by HHL. The performance of HHL for A-matrices appearing in DCOPF problems is discussed. The initialization of HHL for encoding data from classical data to a quantum state in an efficient manner is also investigated. The impact of HHL calculation error on DCOPF convergence and solution accuracy is analyzed. Qiskit module is used to test the HHL-based DCOPF problem on a 3-bus system. The impact of quantum computers and HHL errors on DCOPF is simulated for the IEEE 14- bus system.

DOI
10.1109/tpec56611.2023.10078612

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Harrow-Hassidim-Lloyd (HHL) is a quantum computation algorithm that can solve a system of linear equations in a logarithmic time scale; hence, an exponential speed-up over best-known classical computers, which have polynomial time complexity, is accessible. This paper studies the integration of HHL into the DC optimal power flow problem. Optimality conditions are formulated as a system of equations in the form of Ax=bAx=bAx=b that is solved by HHL. The performance of HHL for A-matrices appearing in DCOPF problems is discussed. The initialization of HHL for encoding data from classical data to a quantum state in an efficient manner is also investigated. The impact of HHL calculation error on DCOPF convergence and solution accuracy is analyzed. Qiskit module is used to test the HHL-based DCOPF problem on a 3-bus system. The impact of quantum computers and HHL errors on DCOPF is simulated for the IEEE 14- bus system.
In this paper, we model and solve a fundamental power system problem, i.e., DC power flow, using a practical quantum computer. The Harrow-Hassidim-Lloyd (HHL) quantum algorithm is used to solve the DC power flow problem. The HHL algorithm for the solution of a system of linear equations (SLE) offers an exponential speedup over the classical computers. The speedup advantage is more significant when the size and the frequency of solving the power flow problem become more substantial. Verified quantum computing applications to power systems are merely nonexistent at this point. Through this paper, we plan to (1) provide a proof-of-concept that practical power system problems can be solved using quantum technology, (2) build a quantum-grid foundation by solving a fundamental power system problem with applications in many other critical grid problems, and (3) apply HHL to solve an SLE which has broad applications in many power system problems. A small 3-bus system is used for testing and demonstration purposes, considering the limitations of the available quantum computing hardware and software. The proposed method's merits and effectiveness are demonstrated using IBM open-source quantum computer and reported through proof-of-concept experimental demonstration using a 4-qubit quantum information processor.
This paper addresses the critical challenge of Op-timal Power Flow (OPF) in electrical engineering, emphasizing the intersection of complexity and technological advancements. Leveraging quantum computation, particularly the Primal-Dual Interior Point Method (PD-IPM) and the Harrow-Hassidim-Lloyd (HHL) algorithm, we explore enhanced solutions for both Alternating Current OPF (ACOPF) and Direct Current OPF (DCOPF). PD-IPM generates linear systems during optimization, aligning with the selected quantum techniques that offer expo-nential speedup. We investigate the scalability and challenges of HHL, emphasizing the current limitations for larger power systems. Additionally, we introduce a hybrid approach that dynamically transitions between quantum and classical methods to optimize convergence. Our study evaluates the proposed methodology's performance under diverse error conditions, em-phasizing its potential to revolutionize solving times for OPF in power systems.
Practical quantum computing applications to power grids are nonexistent at the moment. This paper investigates how a fundamental grid problem, namely DC power flow, can be solved using quantum computing. Power flow is the most widely used power system analysis technique, either as a stand-alone application or embedded in other applications; therefore, its fast and accurate solution is of utmost significance for grid operators. We base our studies on the Harrow-Hassidim-Lloyd (HHL) quantum algorithm, which has a proven theoretical speedup over classical algorithms in solving a system of linear equations. Practical studies on a quantum computer are conducted using the WSCC 9-bus system.
Quantum computers hold promise for solving problems intractable for classical computers, especially those with high time or space complexity. Practicalquantum advantagecan be said to exist for such problems when the end-to-end time for solving such a problem using a classical algorithm exceeds that required by a quantum algorithm. Reducing the power flow (PF) problem into a linear system of equations allows for the formulation of quantum PF (QPF) algorithms, which are based on solving methods for quantum linear systems such as the Harrow-Hassidim-Lloyd (HHL) algorithm. Speedup from using QPF algorithms is often claimed to be exponential when compared to classical PF solved by state-of-the-art algorithms. We investigate the potential for practical quantum advantage in solving QPF compared to classical methods on gate-based quantum computers. Notably, this paper does not present a new QPF solving algorithm but scrutinizes the end-to-end complexity of the QPF approach, providing a nuanced evaluation of the purported quantum speedup in this problem. Our analysis establishes a best-case bound for the HHL-based quantum power flow complexity, conclusively demonstrating that the HHL-based method has higher runtime complexity compared to the classical algorithm for solving the direct current power flow (DCPF) and fast decoupled load flow (FDLF) problem. Notably, our analysis and conclusions can be extended to any quantum linear system solver with rigorous performance guarantees, based on the known complexity lower bounds for this problem. Additionally, we establish that for potential practical quantum advantage (PQA) to exist it is necessary to consider DCPF-type problems with a very narrow range of condition number values and readout requirements.
The rapid integration of renewable energy resources presents formidable challenges in managing power grids. While advanced computing and machine learning techniques offer some solutions for accelerating grid modeling and simulation, there remain complex problems that classical computers cannot effectively address. Quantum computing, a promising technology, has the potential to fundamentally transform how we manage power systems, especially in scenarios with a higher proportion of renewable energy sources. One critical aspect is solving large-scale linear systems of equations, crucial for power system applications like power flow analysis, for which the Harrow-Hassidim-Lloyd (HHL) algorithm is a well-known quantum solution. However, HHL quantum circuits often exhibit excessive depth, making them impractical for current Noisy-Intermediate-Scale-Quantum (NISQ) devices. In this paper, we introduce a versatile framework, powered by NWQSim, that bridges the gap between power system applications and quantum linear solvers available in Qiskit. This framework empowers researchers to efficiently explore power system applications using quantum linear solvers. Through innovative gate fusion strategies, reduced circuit depth, and GPU acceleration, our simulator significantly enhances resource efficiency. Power flow case studies have demonstrated up to a eight-fold speedup compared to Qiskit Aer, all while maintaining comparable levels of accuracy.
The development of quantum processors for practical fluid flow problems is a promising yet distant goal. Recent advances in quantum linear solvers have highlighted their potential for classical fluid dynamics. In this study, we evaluate the Harrow–Hassidim–Lloyd (HHL) quantum linear systems algorithm (QLSA) for solving the idealized Hele–Shaw flow. Our focus is on the accuracy and computational cost of the HHL solver, which we find to be sensitive to the condition number, scaling exponentially with problem size. This emphasizes the need for preconditioning to enhance the practical use of QLSAs in fluid flow applications. Moreover, we perform shots-based simulations on quantum simulators and test the HHL solver on superconducting quantum devices, where noise, large circuit depths, and gate errors limit performance. Error suppression and mitigation techniques improve accuracy, suggesting that such fluid flow problems can benchmark noise mitigation efforts. Our findings provide a foundation for future, more complex application of QLSAs in fluid flow simulations.